Congratulations, you are going to Italy and Greece.  

Try to pack light because there is a lot of traveling and the smaller airlines between islands have crazy luggage charges (Delta flights checked bags are included up to 50 pounds).  Hotels will be able to wash some clothes in the middle of the trip either way and you will probably end up bringing some stuff back.  Call your phone company before you leave to get International Plan then try to use wifi as much as you can to avoid roaming charges.  Also, for credit and ATM cards just check with bank for any fees because some charge an extra 3% for charges in euros.  Otherwise most other places prices besides restaurants and hotels will be very negotiable if dealing in cash. 

Please let us know if you have any questions before or during the trip.